Problem: Solve for $x$ and $y$ using elimination. ${4x-3y = 12}$ ${-x-4y = -41}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${4x-3y = 12}$ $-4x-16y = -164$ Add the top and bottom equations together. $-19y = -152$ $\dfrac{-19y}{{-19}} = \dfrac{-152}{{-19}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {4x-3y = 12}\thinspace$ to find $x$ ${4x - 3}{(8)}{= 12}$ $4x-24 = 12$ $4x-24{+24} = 12{+24}$ $4x = 36$ $\dfrac{4x}{{4}} = \dfrac{36}{{4}}$ ${x = 9}$ You can also plug ${y = 8}$ into $\thinspace {-x-4y = -41}\thinspace$ and get the same answer for $x$ : ${-x - 4}{(8)}{= -41}$ ${x = 9}$